Season the brisket lightly all over with salt and set on a plate near the stove. Heat the canola oil in a Dutch oven over medium-high heat. Once hot, place the brisket into the pot fat cap side down and sear until golden brown, about 4 minutes. Sear the remaining sides until golden, about 3 minutes per side. Transfer the seared brisket back to the plate. Turn off the heat and drain the fat into a bowl.
Add the chicken broth, wine, ½ cup lemon juice, orange juice, lime juice, garlic, bay leaves and black pepper into the Dutch oven; stir to bring up any browned bits.
Place the seared brisket back into the Dutch oven, turn the heat up to a simmer, cover and cook, turning the brisket occasionally, until very tender, but not falling apart, about 2 hours. (Check occasionally to make sure the liquid is simmering, not boiling.) Transfer the brisket to a cutting board; let rest for 15 minutes. Save about ½ cup of the braising liquid in a small bowl.
Thinly shave the fennel on a mandoline or with a sharp chef's knife. Add fennel to a large mixing bowl along with the shallot, orange zest, lime zest, the remaining 3 tablespoons lemon juice and a big pinch of salt. Toss well, then add the olive oil and butter lettuce and toss again.
Thinly slice the brisket against the grain and transfer to the plates with the salad.